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The experimental result of the double Stern-Gerlach experiment to test some quantum measurement theories

Yoshié Otake, S. Tasaki, Tooru Ebisawa, Takeshi Kawai, H. Funahashi

Published Jan 1, 1997• 0 citations
OpenAlex

Abstract

The successful results of phase echo multilayer mirror interferometer for cold neutrons at C3-1-2 (MINE) in JRR3M of JAERI-Tokai enable us to perform `double Stern Gerlach` (dSG) experiment which was proposed by Machida and Namiki in 1987 to test the quantum mechanical measurement theories, especially Many World Interpretation of Everett`s, Environment Theory by Zurek and Many-Hilbert-Space Theory (MHST) by themselves. There are many measurement theories where they don`t distinguish the two steps, a spectral decomposition step and a detection step, through the measurement process while they explain how to derive the wave function reduction theoretically. In MHST they proposed these two steps and clarify the issue of the coherence during the measurement process. This experiment can clarify not only these three theories but also the fact whether these two steps function differently during the measurement process in terms of coherence phenomena. This experiment consists of two spectral decomposition (two magnetic mirrors to divide each beam into two spatially divided beams according to its spin states) put after the simple beam splitter. We investigate the existence of the coherence in the super posed beam after the spectral decomposition. Clear coherence patters are measured with rotating the second composite mirror. This clarifies that the spectral decomposition never plays any role to decrease the coherence between the eigenstates of the superposed state and that we have to investigate the detection step to find the mechanism of the wave packet reduction during the measurement process. (author)

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The successful results of phase echo multilayer mirror interferometer for cold neutrons at C3-1-2 (MINE) in JRR3M of JAERI-Tokai enable us to perform double Stern Gerlach (dSG) experiment which was proposed by Machida and Namiki in 1987 to test the quantum mechanical measurement theories, especially Many World Interpretation of Everetts, Environment Theory by Zurek and Many-Hilbert-Space Theory (MHST) by themselves. There are many measurement theories where they dont distinguish the two steps, a spectral decomposition step and a detection step, through the measurement process while they explain how to derive the wave function reduction theoretically. In MHST they proposed these two steps and clarify the issue of the coherence during the measurement process. This experiment can clarify not only these three theories but also the fact whether these two steps function differently during the measurement process in terms of coherence phenomena. This experiment consists of two spectral decomposition (two magnetic mirrors to divide each beam into two spatially divided beams according to its spin states) put after the simple beam splitter. We investigate the existence of the coherence in the super posed beam after the spectral decomposition. Clear coherence patters are measured with rotating the second composite mirror. This clarifies that the spectral decomposition never plays any role to decrease the coherence between the eigenstates of the superposed state and that we have to investigate the detection step to find the mechanism of the wave packet reduction during the measurement process. (author)
We show that it is possible to explain the quantum measurement process within the framework of quantum mechanics without any additional postulates. The key concept of the theory is decoherence, which appears as an inherent characteristic of quantum mechanics and results from the uncertainty relation. In contrast to environment-induced decoherence, this decoherence exists prior to a measurement being made. To clarify our idea, we examine three elemental experiments: a Stern-Gerlach-like experiment, the Einstein-Podolsky-Rosen-Bohm (EPR-Bohm) experiment, and the double-slit experiment. By considering the first experiment, we explain how the uncertainty relation between position and momentum introduces decoherence prior to measurement. Consideration of the EPR-Bohm experiment leads us to conclude that the correlation of the EPR pair is not a consequence of what is known as the collapse of the wave function. Our theory of decoherence can also be applied to experiments with continuous eigenvalues, such as the double-slit experiment. Consideration of the double-slit experiment leads us to understand how pure quantum mechanics describes the fact that quanta behave as interfering particles.
We present an analytical solution to the decoherence time for the spin measurement and the diagonalization of the density matrix of spin variables in the Stern-Gerlach experiment.This solution requires the calculation of the Pauli spinor with a spatial extension, which is not found in quantum mechanics textbooks.With this full spinor and the measured position of the particle we demonstrate the three postulates of quantum measurement: quantization, spectral decomposition and wave function reduction.The transition from a quantum superposition to a statistical mixture is well explained in this way, but not the single result that always emerges from a particular experiment.The spinor spatial extension also allows the introduction of the de Broglie-Bohm trajectories which give a very simple explanation of the particles' impact.
The theory of measurement is reasonably interpreted without any abrupt and noncausal change of a state, namely, with no “reduction of a wave packet”, in the framework of quantum mechanics. Though a process of measurement is causal in the usual quantum-mechanical sense, it is possible to utilize the concept of the “reduction of a wave packet” without any loss of compatibility. The Stern-Gerlach experiment is put to a careful study to show that the present interpretation is consistent with experiment.
We show that it is possible to explain the quantum measurement process within the framework of quantum mechanics without any additional postulates. The key concept of the theory is decoherence, which appears as an inherent characteristic of quantum mechanics and results from the uncertainty relation. In contrast to environment-induced decoherence, this decoherence exists prior to a measurement being made. To clarify our idea, we examine three elemental experiments: a Stern-Gerlach-like experiment, the Einstein-Podolsky-Rosen-Bohm (EPR-Bohm) experiment, and the double-slit experiment. By considering the first experiment, we explain how the uncertainty relation between position and momentum introduces decoherence prior to measurement. Consideration of the EPR-Bohm experiment leads us to conclude that the correlation of the EPR pair is not a consequence of what is known as the collapse of the wave function. Our theory of decoherence can also be applied to experiments with continuous eigenvalues, such as the double-slit experiment. Consideration of the double-slit experiment leads us to understand how pure quantum mechanics describes the fact that quanta behave as interfering particles.
In most theories of the quantum measurement process changes in an observer’s perception of a state can take place without forces, as for example if a state is prepared in an eigenstate of JxJ_xJx​ (x component of angular momentum) but JzJ_zJz​ is measured. In the “special state” theory (explained in the previous article) any change in wave function requires forces. This allows experimental tests to distinguish these ideas and in the present article two examples of such tests are considered. The first is a kind of double Stern–Gerlach experiment, the second a check for angular momentum changes in a polarizer.
The Stern-Gerlach experiment, a seminal quantum physics experiment, demonstrated the intriguing phenomenon of particle spin quantization, leading to applications in matter-wave interferometry and weak-value measurements. Over the years, several optical experiments have exhibited similar behavior to the Stern-Gerlach experiment, revealing splitting in both spatial and angular domains. Here we show, theoretically and experimentally, that the Stern-Gerlach effect can be extended into the time and frequency domains. By harnessing Kerr nonlinearity in optical fibers, we couple signal and idler pulses using two pump pulses, resulting in the emergence of two distinct eigenstates whereby the signal and idler are either in phase or out of phase. This nonlinear coupling emulates a synthetic magnetization, and by varying it linearly in time, one eigenstate deflects towards a higher frequency, while the other deflects towards a lower frequency. This effect can be utilized to realize an all-optical, phase-sensitive frequency beam splitter, establishing a new paradigm for classical and quantum data processing of frequency-bin superposition states.